Transmission eigenvalues and the bare conductance in the crossover to Anderson localization

Abstract

We measure the field transmission matrix t for microwave radiation propagating through random waveguides in the crossover to Anderson localization. From these measurements, we determine the dimensionless conductance, g, and the individual eigenvalues ${\tau }_n$ of the transmission matrix $t{t}^{†}$ whose sum equals g. In diffusive samples, the highest eigenvalue, ${\tau }_1$, is close to unity corresponding to a transmission of nearly 100%, while for localized waves, the average of ${\tau }_1$, is nearly equal to g. We find that the spacing between average values of $\ln {\tau }_n$ is constant and demonstrate that when surface interactions are taken into account it is equal to the inverse of the bare conductance.

5 pages, 5 figures

References in corpus (2)

• Universal optimal transmission of light through disordered materials
• Dynamics of weakly localized waves

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